Conventionally, spectroscopic measuring devices are used to determine concentrations of absorbing gases in a measured gas mixture. For example, the gas mixture to be measured can be ambient air in which the concentrations of absorbing gases shall be determined. Absorbing gases are the general term for gaseous compounds absorbing light in a particular wavelength range. For example, trace gases such as NO, NO2, NO3 or O3 are covered by the term “absorbing gases”. Particularly the concentrations of such trace gases are frequently measured using corresponding spectroscopic measuring devices. The basic principle of all spectroscopic measuring devices is that each absorbing gas, due to its characteristic molecule structure, has a particular absorption structure when excited by light. If a molecule of such an absorbing gas is excited by a light source emitting light with a wavelength-dependent light intensity over a particular spectral width, i.e. a particular wavelength range, this molecule will absorb a portion of this light corresponding to its specific absorption spectrum, wherein the portion of the absorbed light depends on the wavelength. Accordingly, the absorption spectrum defines the wavelength-dependent absorption characteristic of an absorbing gas regarding the absorption of light. When light from a light source is emitted to a gas mixture whereby the light travels a light path in the gas mixture, then according to the specific absorption spectrum of the absorbing gas more light intensity is absorbed if the light hits more molecules of the absorbing gas on its light path. The light intensity measured after the light emitted from a light source has traveled a certain light path in a particular gas mixture with a particular absorbing gas, depends accordingly on both the path length of the light path and the concentration of the absorbing gas in the gas mixture. Mathematically, this basic principle can be described using the Beer-Lambert law: I=I0*exp[−σ*x*L], where I is the light intensity after it traveled the light path in the gas mixture, I0 is the light intensity emitted from the light source to the gas mixture, σ is the absorption cross section of the trace gas, x is the concentration of the trace gas and L is the path length of the light path. The absorption cross section of a trace gas of course depends on the wavelength and precisely represents the absorption spectrum of a trace gas.
In the light of this basic principle, conventional spectroscopic measuring devices are always designed as an assembly in which light emitted from a light source travels a predetermined or determinable light path, whereat the end of the light path a detector is arranged which can measure the light intensity. For the implementation of spectroscopic measuring devices various, very different options are known. For example, there are spectroscopic measuring devices in which the light path and hence also the path length of the light path is geometrically fixed by a geometric arrangement of mirrors between a starting point and a destination point. In order to guarantee high measuring accuracy, spectroscopic measuring devices are known having a geometrically fixed light path of several kilometers length. Spectroscopic measuring devices with a measuring cell that comprises an optical resonator follow a completely different approach. The optical resonator is located in the measuring cell and comprises a mirror arrangement to reflect light within the mirror arrangement as often as possible. With such a setup, the light path is not geometrically predefined, but depends for example on the reflectivity of the mirror arrangement and on the absorption of light inside the measuring cell. The higher the reflectivity of the mirror assembly and the lower the absorption, the longer the light path. The absorption can be caused for example by components of the gas mixture, such as the contained trace gases, and/or by the absorption behavior of the mirror arrangement. In such measuring devices comprising an optical resonator, the light intensity coupled out from the measuring cell is measured by a detector. The uncoupling can be accomplished for example using a partially transparent beam splitter in the measuring cell or a partially transparent mirror of the mirror arrangement. Since the light path is not geometrically pre-known, calibration measurements are required so that conclusions on the concentration of absorbing gases in the gas mixture provided in the measuring cell can be drawn from a measured light intensity. Through these calibration measurements a value is determined that characterizes the path length of the light path, for example an “average path length”, a “reflectivity” of the mirror arrangement or an “average residence time” of the light in the measuring cell. The options described for the characterization of the path length are equivalent and can be converted into each other. In comparison to the above-described exemplary measuring devices with a fixed geometrical light path, measuring devices comprising an optical resonator have the important advantage that due to the multiple reflections in the optical resonator, a light path can be obtained which is sufficiently long to allow a precise measurement of absorbing gases in a gas mixture, even at a small overall size of the resonator and hence the entire spectroscopic measuring device. As a result, such spectroscopic measuring devices are especially suitable also for local, i.e. spatially resolved measurements of absorbing gas concentrations and are also inexpensive and easy to manufacture.
The present invention relates to such described spectroscopic measuring devices comprising an optical resonator and a method for determining concentrations of absorbing gases in a gas mixture using such spectroscopic measuring devices. Hereby the concentrations of the absorbing gases are determined on the basis of wavelength-dependent measurement values of the light intensity output from the detector. Therefore the read out of the wavelength-dependent measurement values is illustrated as a wavelength-dependent shape of the light intensity a wavelength-dependent measurement value function and where a theoretical wavelength-dependent function according to physical laws is defined, in which function the concentrations are included as selectable parameters, wherein the concentrations are determined by a mathematical fitting algorithm between the theoretical function and the measurement value function. The wavelength-dependent measurement value function is directly calculated from the measurement read out values from the detector and reflects a shape of numerical values that merely depend on the wavelength. For example, the wavelength-dependent measurement value function can be directly defined as a shape of the measured light intensity in dependence of the wavelength. For example, the wavelength-dependent function can be defined by each of the read-out wavelength-dependent measurement values for the light intensity being multiplied by a constant factor or added to a constant summand from which a function value is calculated, wherein this function value is represented in dependence of the wavelength as wavelength-dependent measurement value function.
While a suitable measurement value function can be directly obtained from the measurement values using rather simple arithmetic, the formulation of a useful theoretical function and performing a curve fitting calculation turned out to be difficult. Therefore, it should be taken into account that during the curve fitting calculation, always a numerical variation of the concentrations as a freely selectable and thus fitted parameters of the function must be carried out until the theoretical function is sufficiently well approximated in its shape to the measurement value function. Only, when a sufficiently well approximation between the theoretical function and the measurement value function has been achieved by a corresponding selection of the concentrations as fitted parameters of the theoretical function, one can assume that the concentrations determined in the curve fitting calculation in fact reflect the concentrations of the absorbing gases in the gas mixture. For the assessment when the theoretical function is sufficiently well approximated to the measurement value function, methods known in error calculation are applied such as the determination of the root mean square deviation.
To ensure that such a curve fitting calculation can be numerically performed at all, it is required that the theoretical function has a dependency on the concentrations as parameters to be fitted, which is simple enough to perform a sufficiently good approximation of the theoretical function to the measurement value function through a numerical selection of the concentrations. At the same time, however, the theoretical function must describe the physically expected measurement value function as exactly as possible, in accordance with the physical laws. This is where the problem exists in conventional methods for determining the concentrations of the absorbing gases for spectroscopic measuring devices comprising an optical resonator and concerns the present invention.
Because in such spectroscopic measuring devices, a physically expected measurement value function can be exactly described only by means of very complex mathematical functions, since the formulation of corresponding theoretical functions requires that boundary conditions inherent to such spectroscopic measuring devices are taken into account. On the one hand, the measured light intensity is dependent on the concentration of the absorbing gases and the average path length the light travels inside the measuring cell. The longer the light path at a constant concentration of the absorbing gases, the stronger the absorption in the measuring cell and lower the measured light intensity. On the other hand, the light path depends on both the state of the measuring device (e.g. orientation of the mirror assembly of the resonator and reflectivity of the mirrors, i.e. in particular also contamination of the mirrors) and also the concentrations of the absorbing gases themselves, since the more light is absorbed in the measuring cell, i.e. the greater the concentrations of the absorbing gases, the shorter becomes the average path length. Moreover, the measured light intensity also depends on the properties of the detector that can typically be represented by an instrument function, which characterizes the detector and the entire spectroscopic measuring device. This dependency of the spectroscopic measuring device of instrument functions is relevant for the physically correct presentation of the theoretical function, since both the absorber structures of many absorbing gases and also the properties of the spectroscopic measuring device (especially the reflectivity of the mirrors of the resonator) very strongly depend on the wavelength. Accordingly, a physically correct representation of the theoretical function initially requires a formulation of the expected measurement value function according to physical laws concerning the travel of the light, i.e. the light path, in the measuring cell and thereafter a convolution of this formulation with the instrument function in order to take account of the measuring properties of the measuring device, especially the detector of the measuring device.
In view of the above-described difficulties in the formulation of a physically exact and yet numerically adjustable function, various approximations have been made in state of the an applications in order to achieve a theoretical function that can be used for curve fitting calculation with the measurement value function. One common approach is to define the measurement value function as
      M    ⁡          (      λ      )        =                              I          0                ⁡                  (          λ          )                            I        ⁡                  (          λ          )                      -    1  and the theoretical function as
            T      ⁡              (        λ        )              =                            L          0                ⁡                  (          λ          )                    *                        ∑          i                ⁢                                  ⁢                              ɛ            i                    ⁡                      (            λ            )                                ,where I0(λ) is the wavelength-dependent shape of an initial light intensity, I(λ) is the wavelength-dependent shape of the light intensity resulting from the measurement values during the measurement for determining the concentrations, L0 is a device path length and εi represents the extinction coefficients of the i different absorbing gases. Here εi is frequently expressed as xi*σi, where xi is the concentration of a particular one of the i different assumed absorbing gases and σi is the absorption cross section of the particular absorbing gas known from literature. In common methods using this approximation and performing the fitting calculation where M(λ) is set equal to T(λ), I0(λ) and L0 are initially determined in calibration measurements. I0(λ) is the initial light intensity measured by the detector when “zero air” is arranged in the measuring cell. Normally, preferably clean air is used as zero air, for example ambient air that has been filtered by aerosol filters for the removal of scattering aerosols and/or by additional filters for the removal of absorbers. For example, N2, 02 or a N2-02 mixture can also be used as zero air. Different calibration measurements and various methods for performing such calibration measurements are known for the determination of L0. According to one method, an average path length of the light path in the measuring cell is determined L0(λ) by flooding the measuring cell with helium for a first measurement and with zero air for a second measurement. In both measurements, the light intensity is measured at the exit of the measuring cell. As it can be assumed that the differences between the light intensities measured in the first and the second measurements are largely based on a different Rayleigh scattering in air and helium, which respectively depends on the Rayleigh scattering cross section and hence on the molecule size in air or helium, an average path length of the light path and thus the device path length I0(λ) can be obtained from:
                    L        0            ⁡              (        λ        )              =                                                      I              Luft                        ⁡                          (              λ              )                                                          I              He                        ⁡                          (              λ              )                                      -        1                                          ɛ            He                    ⁡                      (            λ            )                          -                              ɛ            Luft                    ⁡                      (            λ            )                                ,where ILuft is the measured light intensity when flushing the measuring cell with zero air, IHe is the measured light intensity when flushing the measuring cell with helium, and εHe and εLuft are the Rayleigh extinction coefficients, wherein the extinction coefficient is calculable from ε=σ*n, where σ is the Rayleigh cross section sufficiently documented in the literature and n is the particle number density that can be calculated in good approximation using the ideal gas law at a known pressure and temperature. Another method is to flood the measuring cell with a gas mixture containing a pre-known concentration of a particular trace gas. It is then possible to directly draw a conclusion on the average path length of the light path from the measured light intensity and the known absorption structure of the trace gas and thus determine the device path length. This method, however, can only provide information about the wavelength dependency of the path length of the light path within the wavelength range of the absorption structure of the particular trace gas. If lasers are used as a light source for the spectroscopic measuring device, there is another known method for the calibration measurement in which the decay constant of the light intensity is determined after the laser is switched on or off. The decay constant can be determined by:
            I      ⁡              (        t        )              =                  I        ⁡                  (                      t            0                    )                    *              exp        ⁡                  [                                    -                              c                                  L                  0                                                      ⁢                          (                              t                -                                  t                  0                                            )                                ]                      ,wherein I is the measured light intensity, I0 is a particular time (after switch-off), c is the light speed and L0 is an average path length of the light path, i.e. the device path length. The decay constant is expressed as
      c          L      0        .
The conventional method described for the determination of concentrations of absorbing gases, in which the measurement value function M(λ) is set equal with the theoretical function T(λ) with the definition
                                          I            0                    ⁡                      (            λ            )                                    I          ⁡                      (            λ            )                              -      1        =                            L          0                ⁡                  (          λ          )                    *                        ∑          i                ⁢                              ɛ            i                    ⁡                      (            λ            )                                ,can only lead to an approximately correct determination of the concentration if 1.) only a relatively low absorption of light occurs in the measuring cell or if the measurement values are measured using a very expensive detector with a very high spectral resolution, i.e. resolution regarding the wavelength, and 2.) the state of the measuring device at the determination of I(λ) is identical with the state during the determination of I0(λ), because only then the mathematical approximations that have been performed in the determination of the described relation for performing the curve fitting calculation based on physical laws are correct. In any case, the second condition can be achieved only with considerable effort. Because on the one hand, the properties of the optical assembly of the measuring device, especially the measuring cell, may vary as a consequence of a misalignment, contamination of the mirror assembly or due to misalignment of the lens arrangements so that the measurements of I0(λ) and I(λ) must preferably be performed in immediate succession so that the initial measurement of I0(λ) must preferably be performed prior to each new measurement for the determination of concentrations in a gas mixture. On the other hand, for conventionally used light sources, the intensity emitted from the light source considerably varies already within short time intervals. Considering, however, that for applying the described relation, it is an absolutely requirement that the spectroscopic measuring device and particularly also the light source are in the same state to determine the concentration of absorbing gases, thus complex measures must be applied in conventional methods to stabilize the emitted intensity from the light. Such measures are frequently insufficient, on the one hand, and expensive on the otherhand.
Furthermore, conventional methods exist for the determination of concentrations of absorbing gases in which the measurement value function M(λ) is represented by
      M    ⁡          (      λ      )        =      ln    ⁡          (                                    I            0                    ⁡                      (            λ            )                                    I          ⁡                      (            λ            )                              )      and the theoretical function is represented
            T      ⁡              (        λ        )              =                                        L            eff                    ⁡                      (            λ            )                          *                              ∑            i                    ⁢                                    ɛ              i                        ⁡                          (              λ              )                                          +      A        ,where M(λ) is set equal to T(λ) performing the curve fitting calculation. In this equation, L0(λ), I(λ) and εi(λ) are the above-stated physical parameters. Leff(λ) is an “effective path length”, i.e. the average path length the light travels in the measuring cell in the gas mixture with the absorbers. While L0(λ) is the average path length during a calibration measurement, as explained above, Leff(λ) is the average path length during the measurement for determining the concentrations. The summand A is a parameter that can be freely selected during the curve fitting calculation and by which the device properties can be taken into account. Compared to the first-mentioned conventional method, this conventional method has the advantage that a variation of the light intensity emitted from the light source between the time of the initial measurement for deter mining the initial light intensity and the time of the actual measurement for determining the light intensity for the concentrations of the absorbing gases does not directly lead to a faulty curve fitting calculation, because due to the logarithmic expression of M(λ), a variation by the factor q “is included” in the selectable summand A, since ln
      (                            I          0                ⁡                  (          λ          )                            q        *                  I          ⁡                      (            λ            )                                )    =            ln      ⁡              (                                            I              0                        ⁡                          (              λ              )                                            I            ⁡                          (              λ              )                                      )              -          ln      ⁢                          ⁢              q        .            
However, in this conventional method, it problem to determine the effective path length Leff(λ), which physically depends on the concentrations of the absorbing gases themselves, as discussed above. Usually, this effective path length is approximated by assuming that Leff(λ)=L0(λ)*K(λ), where L0(λ) represents the above described path length and K(λ) represents a correction factor calculated using
      K    ⁡          (      λ      )        =                    ln        ⁡                  (                                                    I                0                            ⁡                              (                λ                )                                                    I              ⁡                              (                λ                )                                              )                                                                I              0                        ⁡                          (              λ              )                                            I            ⁡                          (              λ              )                                      -        1              .  Through this definition of the effective path length, the correctness of the fitting calculation becomes, however, again dependent on whether the state of the spectroscopic measuring device at the determination of I0(λ) was identical with the state at the determination of I(λ), because only then it can be assumed that the determination of K(λ) for the determination of the effective path length Leff(λ) is sufficiently correct. Through this calculation of K(λ) from I0(λ) and I(λ), which is usually applied, the method becomes mathematically equivalent to the above-mentioned representation of the measurement value function using
            M      ⁡              (        λ        )              =                                        I            0                    ⁡                      (            λ            )                                    I          ⁡                      (            λ            )                              -      1        ,which can be easily derived by substitution. For this reason, the correctness of the determined concentrations in the above-described conventional method for determining the concentrations of absorbing gases with a spectroscopic measuring device also essentially depends on the condition that the spectroscopic measuring device is kept constant during different measurements. This is complicated and can be hardly implemented free of errors so that even this method involves excessive cost and a high error rate. Additionally, in such methods, even in case of a—hypothetically—perfect match of the state of the measuring device during the two measurements for I0(λ) and I(λ), the calculation of K(λ) is always limited to an accuracy which is defined by the properties of the measuring device, especially the spectral resolution of the detector.